Solve {l}{y=-x/x+1}{xin[-2,-1)}

$$\left. \begin{array} { l } { y = \frac { - x } { x + 1 } } \\ { x \in [ - 2 , - 1 ) } \end{array} \right.$$

Solve for x

$$x=-\frac{y}{y+1}$$

$$y\neq -1$$

Steps for Solving Linear Equation

Variable x cannot be equal to -1 since division by zero is not defined. Multiply both sides of the equation by x+1.

$$y\left(x+1\right)=-x$$

Use the distributive property to multiply y by x+1.

$$yx+y=-x$$

Add x to both sides.

$$yx+y+x=0$$

Subtract y from both sides. Anything subtracted from zero gives its negation.

$$yx+x=-y$$

Combine all terms containing x.

$$\left(y+1\right)x=-y$$

Divide both sides by y+1.

$$\frac{\left(y+1\right)x}{y+1}=-\frac{y}{y+1}$$

Dividing by y+1 undoes the multiplication by y+1.

$$x=-\frac{y}{y+1}$$

Variable x cannot be equal to -1.

$$x=-\frac{y}{y+1}\text{, }x\neq -1$$